There are 5040 ways.
7
27!
19*18*17*16*15 = 1,395,360
For the first spot, you can choose any one of 5 students. For the second spot, you can choose any one of the remaining 4 students. For the third spot, you can choose any one of the remaining 3 students. etc. So the answer is: 5x4x3x2x1 = 120
There are 5040 ways.
53,130 ways.
6,375,600
There are 11880 ways.
They can be selected in 756 ways.
4*3*2*1 = 24 ways.
5! (5 factorial), which is 1 x 2 x 3 x 4 x 5.
7
Well, honey, to select 5 students from a class of 23, you're looking at a good old-fashioned combination problem. So, the number of ways a teacher can select 5 students from a class of 23 is 23 choose 5, which equals 3,359 ways. So, get those students ready to shine on that bulletin board!
27!
333
This is a question of permutation. There are only 3 ways. A-B-C, B-C-A, C-A-B